Find the polynomial having roots at $ 5 $ , $ -\dfrac{ 86 }{ 5 } $ , $ 8 $ , $ 31 $ and $ 2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 5x^5-144x^4-1301x^3+35036x^2-170436x+213280 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 5 $ | $ x-5 $ |
| $ -\dfrac{ 86 }{ 5 } $ | $ 5x+86 $ |
| $ 8 $ | $ x-8 $ |
| $ 31 $ | $ x-31 $ |
| $ 2 $ | $ x-2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-5 \right) \cdot \left( 5x+86 \right) \cdot \left( x-8 \right) \cdot \left( x-31 \right) \cdot \left( x-2 \right) = 5x^5-144x^4-1301x^3+35036x^2-170436x+213280 $$This page was created using
Polynomial From Roots Calculator